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A fundamental problem in machine learning is to understand how neural networks make accurate predictions, while seemingly bypassing the curse of dimensionality. A possible explanation is that common training algorithms for neural networks…

We initiate the study of probabilistic parallel programs with dynamic process creation and synchronisation. To this end, we introduce probabilistic split-join systems (pSJSs), a model for parallel programs, generalising both probabilistic…

In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this paper, we focus on improving the robustness of a large class of learning algorithms that are formulated…

Motivated by what is required for real-time path planning, the paper starts out by presenting sRMPD, a new recursive "local" planner founded on the key notion that, unless made necessary by an obstacle, there must be no deviation from the…

We introduce fast randomized algorithms for solving semidefinite programming (SDP) relaxations of the partial permutation synchronization (PPS) problem, a core task in multi-image matching with significant relevance to 3D reconstruction.…

Accurately monitoring the system's operating point is central to the reliable and economic operation of an electric power grid. Power system state estimation (PSSE) aims to obtain complete voltage magnitude and angle information at each bus…

This paper addresses the question of what exactly is an analogue of the preconditioned steepest descent (PSD) algorithm in the case of a symmetric indefinite system with an SPD preconditioner. We show that a basic PSD-like scheme for an…

Sparse recovery and subset selection are fundamental problems in varied communities, including signal processing, statistics and machine learning. Herein, we focus on an important greedy algorithm for these problems: Backward Stepwise…

State-space models (SSMs) and transformers dominate the language modeling landscape. However, they are constrained to a lower computational complexity than classical recurrent neural networks (RNNs), limiting their expressivity. In…

We present in this paper a generic framework for the analysis of multi-threaded programs with recursive procedure calls, synchronisation by rendez-vous between parallel threads, and dynamic creation of new threads. To this end, we consider…

Sequence models based on linear state spaces (SSMs) have recently emerged as a promising choice of architecture for modeling long range dependencies across various modalities. However, they invariably rely on discretization of a continuous…

Selective state-space models (SSMs) are an emerging alternative to the Transformer, offering the unique advantage of parallel training and sequential inference. Although these models have shown promising performance on a variety of tasks,…

Simulators are a pervasive tool in reinforcement learning, but most existing algorithms cannot efficiently exploit simulator access -- particularly in high-dimensional domains that require general function approximation. We explore the…

HPC systems are a critical resource for scientific research. The increased demand for computational power and memory ushers in the exascale era, in which supercomputers are designed to provide enormous computing power to meet these needs.…

Transformers excel at in-context retrieval but suffer from quadratic complexity with sequence length, while State Space Models (SSMs) offer efficient linear-time processing but have limited retrieval capabilities. We investigate whether…

We reconsider randomized algorithms for the low-rank approximation of symmetric positive semi-definite (SPSD) matrices such as Laplacian and kernel matrices that arise in data analysis and machine learning applications. Our main results…

The recursive least-squares (RLS) algorithm has well-documented merits for reducing complexity and storage requirements, when it comes to online estimation of stationary signals as well as for tracking slowly-varying nonstationary…

Markov decision processes (MDPs) are a standard model for sequential decision-making problems and are widely used across many scientific areas, including formal methods and artificial intelligence (AI). MDPs do, however, come with the…

State-space models (SSMs) face a fundamental trade-off between efficiency and expressivity that is mainly dictated by the structure of the model's transition matrix. Unstructured transition matrices enable maximal expressivity, as measured…

Semantic segmentation is critical for scene understanding but demands costly pixel-wise annotations, attracting increasing attention to semi-supervised approaches to leverage abundant unlabeled data. While semi-supervised segmentation is…